Page:Elementary Text-book of Physics (Anthony, 1897).djvu/188

174 length. The number of vibrations is inversely as the length of the cord, directly as the square root of the tension, and inversely as the square root of the mass per unit length.

149. Transverse Vibrations of Rods, Plates, etc.—The vibrations of rods, plates, and bells are all cases of stationary waves resulting from systems of waves travelling in opposite directions. Subdivision into segments occurs, but in these cases the relations of the various overtones are not so simple as in the cases before considered. For a rod fixed at one end, sounding its fundamental tone, there is a node at the fixed end only. For the first overtone there is a second node near the free end of the rod, and the number of vibrations is a little more than six times the number for the fundamental.

A rod free at both ends has two nodes when sounding its fundamental, as shown in Fig. 55. The distance of these nodes from the ends is about $$\tfrac{2}{9}$$ the length of the rod. If the rod be bent, the nodes approach the centre until, when it has assumed the $$\text{U}$$ form like a tuning-fork, the two nodes are very near the centre. This will be understood from Fig. 56.

The nodal lines on plates may be shown by fixing the plate in a horizontal position and sprinkling sand over its surface. When the plate is made to vibrate, the sand gathers at the nodes and marks their position. The figures thus formed are known as Chladni's figures.

150. Resonance.—If several pendulums be suspended from the